中华经济学子奇才David X. Li: 一个公式7年内改变了世界

加京游子

新手上路
注册
2008-06-18
消息
743
荣誉分数
2
声望点数
28
这里有人认识或听说过此奇才吗?游子今天才看到一篇评论他的文章。要是看了这篇文章,你大概也会认为他是中华经济学人史无前例的奇才的!

教育:南开大学经济学硕士;Laval University MBA; the University of Waterloo master's in actuarial science和Ph. D in statistics

现就职:北京China International Capital Corporation

曾就职:CIBC, JP Morgan Chase, Barclays Capital

凭发表在The Journal of Fixed Income的"On Default Correlation: A Copula Function Approach", David在7年内改变了世界!

要是这场世界性大危机迟来几年,他很可能成为问鼎诺贝尔经济学奖的中华经济学子第一人。现在,只能当这场世界性大危机的理论祖师爷了。流年似水、人生如梦呀!有才有志的后生晚辈们:世界是你们的,也是我们的,但归根到底是你们的!好好干,看你们的了!

这篇改变世界的原文在这里:http://www-m4.ma.tum.de/courses/SS04/seminar/paper/Li2000_default_correlation.pdf

以下是评论他的文章

Recipe for Disaster: The Formula That Killed Wall Street

by Felix Salmon
WIRED MAGAZINE: 17.03
Tech Biz : IT RSS

In the mid-'80s, Wall Street turned to the quants-brainy financial engineers-to invent new ways to boost profits. Their methods for minting money worked brilliantly... until one of them devastated the global economy.

A year ago, it was hardly unthinkable that a math wizard like David X. Li might someday earn a Nobel Prize. After all, financial economists-even Wall Street quants-have received the Nobel in economics before, and Li's work on measuring risk has had more impact, more quickly, than previous Nobel Prize-winning contributions to the field. Today, though, as dazed bankers, politicians, regulators, and investors survey the wreckage of the biggest financial meltdown since the Great Depression, Li is probably thankful he still has a job in finance at all. Not that his achievement should be dismissed. He took a notoriously tough nut-determining correlation, or how seemingly disparate events are related-and cracked it wide open with a simple and elegant mathematical formula, one that would become ubiquitous in finance worldwide.

For five years, Li's formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.

His method was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrenched-and was making people so much money-that warnings about its limitations were largely ignored.

Then the model fell apart. Cracks started appearing early on, when financial markets began behaving in ways that users of Li's formula hadn't expected. The cracks became full-fledged canyons in 2008-when ruptures in the financial system's foundation swallowed up trillions of dollars and put the survival of the global banking system in serious peril.

David X. Li, it's safe to say, won't be getting that Nobel anytime soon. One result of the collapse has been the end of financial economics as something to be celebrated rather than feared. And Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.

How could one formula pack such a devastating punch? The answer lies in the bond market, the multitrillion-dollar system that allows pension funds, insurance companies, and hedge funds to lend trillions of dollars to companies, countries, and home buyers.

A bond, of course, is just an IOU, a promise to pay back money with interest by certain dates. If a company-say, IBM-borrows money by issuing a bond, investors will look very closely over its accounts to make sure it has the wherewithal to repay them. The higher the perceived risk-and there's always some risk-the higher the interest rate the bond must carry.

Bond investors are very comfortable with the concept of probability. If there's a 1 percent chance of default but they get an extra two percentage points in interest, they're ahead of the game overall-like a casino, which is happy to lose big sums every so often in return for profits most of the time.

Bond investors also invest in pools of hundreds or even thousands of mortgages. The potential sums involved are staggering: Americans now owe more than $11 trillion on their homes. But mortgage pools are messier than most bonds. There's no guaranteed interest rate, since the amount of money homeowners collectively pay back every month is a function of how many have refinanced and how many have defaulted. There's certainly no fixed maturity date: Money shows up in irregular chunks as people pay down their mortgages at unpredictable times-for instance, when they decide to sell their house. And most problematic, there's no easy way to assign a single probability to the chance of default.

Wall Street solved many of these problems through a process called tranching, which divides a pool and allows for the creation of safe bonds with a risk-free triple-A credit rating. Investors in the first tranche, or slice, are first in line to be paid off. Those next in line might get only a double-A credit rating on their tranche of bonds but will be able to charge a higher interest rate for bearing the slightly higher chance of default. And so on.

"...correlation is charlatanism"
The reason that ratings agencies and investors felt so safe with the triple-A tranches was that they believed there was no way hundreds of homeowners would all default on their loans at the same time. One person might lose his job, another might fall ill. But those are individual calamities that don't affect the mortgage pool much as a whole: Everybody else is still making their payments on time.

But not all calamities are individual, and tranching still hadn't solved all the problems of mortgage-pool risk. Some things, like falling house prices, affect a large number of people at once. If home values in your neighborhood decline and you lose some of your equity, there's a good chance your neighbors will lose theirs as well. If, as a result, you default on your mortgage, there's a higher probability they will default, too. That's called correlation-the degree to which one variable moves in line with another-and measuring it is an important part of determining how risky mortgage bonds are.

Investors like risk, as long as they can price it. What they hate is uncertainty-not knowing how big the risk is. As a result, bond investors and mortgage lenders desperately want to be able to measure, model, and price correlation. Before quantitative models came along, the only time investors were comfortable putting their money in mortgage pools was when there was no risk whatsoever-in other words, when the bonds were guaranteed implicitly by the federal government through Fannie Mae or Freddie Mac.

Yet during the '90s, as global markets expanded, there were trillions of new dollars waiting to be put to use lending to borrowers around the world-not just mortgage seekers but also corporations and car buyers and anybody running a balance on their credit card-if only investors could put a number on the correlations between them. The problem is excruciatingly hard, especially when you're talking about thousands of moving parts. Whoever solved it would earn the eternal gratitude of Wall Street and quite possibly the attention of the Nobel committee as well.

To understand the mathematics of correlation better, consider something simple, like a kid in an elementary school: Let's call her Alice. The probability that her parents will get divorced this year is about 5 percent, the risk of her getting head lice is about 5 percent, the chance of her seeing a teacher slip on a banana peel is about 5 percent, and the likelihood of her winning the class spelling bee is about 5 percent. If investors were trading securities based on the chances of those things happening only to Alice, they would all trade at more or less the same price.

But something important happens when we start looking at two kids rather than one-not just Alice but also the girl she sits next to, Britney. If Britney's parents get divorced, what are the chances that Alice's parents will get divorced, too? Still about 5 percent: The correlation there is close to zero. But if Britney gets head lice, the chance that Alice will get head lice is much higher, about 50 percent-which means the correlation is probably up in the 0.5 range. If Britney sees a teacher slip on a banana peel, what is the chance that Alice will see it, too? Very high indeed, since they sit next to each other: It could be as much as 95 percent, which means the correlation is close to 1. And if Britney wins the class spelling bee, the chance of Alice winning it is zero, which means the correlation is negative: -1.

If investors were trading securities based on the chances of these things happening to both Alice and Britney, the prices would be all over the place, because the correlations vary so much.

But it's a very inexact science. Just measuring those initial 5 percent probabilities involves collecting lots of disparate data points and subjecting them to all manner of statistical and error analysis. Trying to assess the conditional probabilities-the chance that Alice will get head lice if Britney gets head lice-is an order of magnitude harder, since those data points are much rarer. As a result of the scarcity of historical data, the errors there are likely to be much greater.

In the world of mortgages, it's harder still. What is the chance that any given home will decline in value? You can look at the past history of housing prices to give you an idea, but surely the nation's macroeconomic situation also plays an important role. And what is the chance that if a home in one state falls in value, a similar home in another state will fall in value as well?

Here's what killed your 401(k) David X. Li's Gaussian copula function as first published in 2000. Investors exploited it as a quick-and fatally flawed-way to assess risk. A shorter version appears on this month's cover of Wired.

Probability
Specifically, this is a joint default probability-the likelihood that any two members of the pool (A and B) will both default. It's what investors are looking for, and the rest of the formula provides the answer.

Survival times

The amount of time between now and when A and B can be expected to default. Li took the idea from a concept in actuarial science that charts what happens to someone's life expectancy when their spouse dies.

Equality

A dangerously precise concept, since it leaves no room for error. Clean equations help both quants and their managers forget that the real world contains a surprising amount of uncertainty, fuzziness, and precariousness.

Copula

This couples (hence the Latinate term copula) the individual probabilities associated with A and B to come up with a single number. Errors here massively increase the risk of the whole equation blowing up.

Distribution functions

The probabilities of how long A and B are likely to survive. Since these are not certainties, they can be dangerous: Small miscalculations may leave you facing much more risk than the formula indicates.

Gamma

The all-powerful correlation parameter, which reduces correlation to a single constant-something that should be highly improbable, if not impossible. This is the magic number that made Li's copula function irresistible.


Enter Li, a star mathematician who grew up in rural China in the 1960s. He excelled in school and eventually got a master's degree in economics from Nankai University before leaving the country to get an MBA from Laval University in Quebec. That was followed by two more degrees: a master's in actuarial science and a PhD in statistics, both from Ontario's University of Waterloo. In 1997 he landed at Canadian Imperial Bank of Commerce, where his financial career began in earnest; he later moved to Barclays Capital and by 2004 was charged with rebuilding its quantitative analytics team.

Li's trajectory is typical of the quant era, which began in the mid-1980s. Academia could never compete with the enormous salaries that banks and hedge funds were offering. At the same time, legions of math and physics PhDs were required to create, price, and arbitrage Wall Street's ever more complex investment structures.

In 2000, while working at JPMorgan Chase, Li published a paper in The Journal of Fixed Income titled "On Default Correlation: A Copula Function Approach." (In statistics, a copula is used to couple the behavior of two or more variables.) Using some relatively simple math-by Wall Street standards, anyway-Li came up with an ingenious way to model default correlation without even looking at historical default data. Instead, he used market data about the prices of instruments known as credit default swaps.

If you're an investor, you have a choice these days: You can either lend directly to borrowers or sell investors credit default swaps, insurance against those same borrowers defaulting. Either way, you get a regular income stream-interest payments or insurance payments-and either way, if the borrower defaults, you lose a lot of money. The returns on both strategies are nearly identical, but because an unlimited number of credit default swaps can be sold against each borrower, the supply of swaps isn't constrained the way the supply of bonds is, so the CDS market managed to grow extremely rapidly. Though credit default swaps were relatively new when Li's paper came out, they soon became a bigger and more liquid market than the bonds on which they were based.

When the price of a credit default swap goes up, that indicates that default risk has risen. Li's breakthrough was that instead of waiting to assemble enough historical data about actual defaults, which are rare in the real world, he used historical prices from the CDS market. It's hard to build a historical model to predict Alice's or Britney's behavior, but anybody could see whether the price of credit default swaps on Britney tended to move in the same direction as that on Alice. If it did, then there was a strong correlation between Alice's and Britney's default risks, as priced by the market. Li wrote a model that used price rather than real-world default data as a shortcut (making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly).

It was a brilliant simplification of an intractable problem. And Li didn't just radically dumb down the difficulty of working out correlations; he decided not to even bother trying to map and calculate all the nearly infinite relationships between the various loans that made up a pool. What happens when the number of pool members increases or when you mix negative correlations with positive ones? Never mind all that, he said. The only thing that matters is the final correlation number-one clean, simple, all-sufficient figure that sums up everything.

The effect on the securitization market was electric. Armed with Li's formula, Wall Street's quants saw a new world of possibilities. And the first thing they did was start creating a huge number of brand-new triple-A securities. Using Li's copula approach meant that ratings agencies like Moody's-or anybody wanting to model the risk of a tranche-no longer needed to puzzle over the underlying securities. All they needed was that correlation number, and out would come a rating telling them how safe or risky the tranche was.

As a result, just about anything could be bundled and turned into a triple-A bond-corporate bonds, bank loans, mortgage-backed securities, whatever you liked. The consequent pools were often known as collateralized debt obligations, or CDOs. You could tranche that pool and create a triple-A security even if none of the components were themselves triple-A. You could even take lower-rated tranches of other CDOs, put them in a pool, and tranche them-an instrument known as a CDO-squared, which at that point was so far removed from any actual underlying bond or loan or mortgage that no one really had a clue what it included. But it didn't matter. All you needed was Li's copula function.

The CDS and CDO markets grew together, feeding on each other. At the end of 2001, there was $920 billion in credit default swaps outstanding. By the end of 2007, that number had skyrocketed to more than $62 trillion. The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006.

At the heart of it all was Li's formula. When you talk to market participants, they use words like beautiful, simple, and, most commonly, tractable. It could be applied anywhere, for anything, and was quickly adopted not only by banks packaging new bonds but also by traders and hedge funds dreaming up complex trades between those bonds.

"The corporate CDO world relied almost exclusively on this copula-based correlation model," says Darrell Duffie, a Stanford University finance professor who served on Moody's Academic Advisory Research Committee. The Gaussian copula soon became such a universally accepted part of the world's financial vocabulary that brokers started quoting prices for bond tranches based on their correlations. "Correlation trading has spread through the psyche of the financial markets like a highly infectious thought virus," wrote derivatives guru Janet Tavakoli in 2006.

The damage was foreseeable and, in fact, foreseen. In 1998, before Li had even invented his copula function, Paul Wilmott wrote that "the correlations between financial quantities are notoriously unstable." Wilmott, a quantitative-finance consultant and lecturer, argued that no theory should be built on such unpredictable parameters. And he wasn't alone. During the boom years, everybody could reel off reasons why the Gaussian copula function wasn't perfect. Li's approach made no allowance for unpredictability: It assumed that correlation was a constant rather than something mercurial. Investment banks would regularly phone Stanford's Duffie and ask him to come in and talk to them about exactly what Li's copula was. Every time, he would warn them that it was not suitable for use in risk management or valuation.


In hindsight, ignoring those warnings looks foolhardy. But at the time, it was easy. Banks dismissed them, partly because the managers empowered to apply the brakes didn't understand the arguments between various arms of the quant universe. Besides, they were making too much money to stop.

In finance, you can never reduce risk outright; you can only try to set up a market in which people who don't want risk sell it to those who do. But in the CDO market, people used the Gaussian copula model to convince themselves they didn't have any risk at all, when in fact they just didn't have any risk 99 percent of the time. The other 1 percent of the time they blew up. Those explosions may have been rare, but they could destroy all previous gains, and then some.

Li's copula function was used to price hundreds of billions of dollars' worth of CDOs filled with mortgages. And because the copula function used CDS prices to calculate correlation, it was forced to confine itself to looking at the period of time when those credit default swaps had been in existence: less than a decade, a period when house prices soared. Naturally, default correlations were very low in those years. But when the mortgage boom ended abruptly and home values started falling across the country, correlations soared.

Bankers securitizing mortgages knew that their models were highly sensitive to house-price appreciation. If it ever turned negative on a national scale, a lot of bonds that had been rated triple-A, or risk-free, by copula-powered computer models would blow up. But no one was willing to stop the creation of CDOs, and the big investment banks happily kept on building more, drawing their correlation data from a period when real estate only went up.

"Everyone was pinning their hopes on house prices continuing to rise," says Kai Gilkes of the credit research firm CreditSights, who spent 10 years working at ratings agencies. "When they stopped rising, pretty much everyone was caught on the wrong side, because the sensitivity to house prices was huge. And there was just no getting around it. Why didn't rating agencies build in some cushion for this sensitivity to a house-price-depreciation scenario? Because if they had, they would have never rated a single mortgage-backed CDO."

Bankers should have noted that very small changes in their underlying assumptions could result in very large changes in the correlation number. They also should have noticed that the results they were seeing were much less volatile than they should have been-which implied that the risk was being moved elsewhere. Where had the risk gone?

They didn't know, or didn't ask. One reason was that the outputs came from "black box" computer models and were hard to subject to a commonsense smell test. Another was that the quants, who should have been more aware of the copula's weaknesses, weren't the ones making the big asset-allocation decisions. Their managers, who made the actual calls, lacked the math skills to understand what the models were doing or how they worked. They could, however, understand something as simple as a single correlation number. That was the problem.

"The relationship between two assets can never be captured by a single scalar quantity," Wilmott says. For instance, consider the share prices of two sneaker manufacturers: When the market for sneakers is growing, both companies do well and the correlation between them is high. But when one company gets a lot of celebrity endorsements and starts stealing market share from the other, the stock prices diverge and the correlation between them turns negative. And when the nation morphs into a land of flip-flop-wearing couch potatoes, both companies decline and the correlation becomes positive again. It's impossible to sum up such a history in one correlation number, but CDOs were invariably sold on the premise that correlation was more of a constant than a variable.

No one knew all of this better than David X. Li: "Very few people understand the essence of the model," he told The Wall Street Journal way back in fall 2005.

"Li can't be blamed," says Gilkes of CreditSights. After all, he just invented the model. Instead, we should blame the bankers who misinterpreted it. And even then, the real danger was created not because any given trader adopted it but because every trader did. In financial markets, everybody doing the same thing is the classic recipe for a bubble and inevitable bust.

Nassim Nicholas Taleb, hedge fund manager and author of The Black Swan, is particularly harsh when it comes to the copula. "People got very excited about the Gaussian copula because of its mathematical elegance, but the thing never worked," he says. "Co-association between securities is not measurable using correlation," because past history can never prepare you for that one day when everything goes south. "Anything that relies on correlation is charlatanism."

Li has been notably absent from the current debate over the causes of the crash. In fact, he is no longer even in the US. Last year, he moved to Beijing to head up the risk-management department of China International Capital Corporation. In a recent conversation, he seemed reluctant to discuss his paper and said he couldn't talk without permission from the PR department. In response to a subsequent request, CICC's press office sent an email saying that Li was no longer doing the kind of work he did in his previous job and, therefore, would not be speaking to the media.

In the world of finance, too many quants see only the numbers before them and forget about the concrete reality the figures are supposed to represent. They think they can model just a few years' worth of data and come up with probabilities for things that may happen only once every 10,000 years. Then people invest on the basis of those probabilities, without stopping to wonder whether the numbers make any sense at all.

As Li himself said of his own model: "The most dangerous part is when people believe everything coming out of it."

Felix Salmon (felix@felixsalmon.com) writes the Market Movers financial blog at Portfolio.com.
 
呵呵,想不到是南开校友。给咱长志气。不过把当前的金融危机归罪到一个统计博士的相关模型上,未免有些夸大其辞。具体根源恐怕几十个诺贝尔奖获得者也解释不清(谁能说清,我相信很快能得诺奖)。不过,Moodys 和S&P这些评级公司过分依靠这些定价模型,草率地给非常复杂的CDS,CDO以简单一个字母A或BBB来表示无风险投资,是此次金融危机的罪魁祸首之一。加上其他配套措施的失误,才酿成百年大错。所以李博士的Gaussian copula function 模型只是个工具,象锤子和锯一样。而泛用此工具忽悠投资者,借以发财的评级公司和投资银行才是罪魁祸首(投行这种金融经营模式也快要自取灭亡了)。有本事还是研究一下如何走出当前的金融和经济危机才是正路。可喜的是,渥太华一些大金融部门的技术人才已经成立了业余研究小组,列出几项课题,群策群力,共同专心一个一个研究。下一个课题就是金融投资中信用风险的测量,分析和管理策略。
 
呵呵,想不到是南开校友。给咱长志气。不过把当前的金融危机归罪到一个统计博士的相关模型上,未免有些夸大其辞。具体根源恐怕几十个诺贝尔奖获得者也解释不清(谁能说清,我相信很快能得诺奖)。

两个字“贪婪”。

(诺奖有多少奖金来着?:D)
 
两个字“贪婪”。

(诺奖有多少奖金来着?:D)
听说诺奖也就才一百五十万美元.如果三个人分享,每人才一套房子钱。还不如中国运动员得奥运会金牌的奖金多。动恼的还是不如动体力的值钱。:D
 
Nobody can have said it better than Dr. Li himself, "The most dangerous part is when people believe everything coming out of it."

The trigger of the ongoing financial and economic crisis, whose presumed severity is not experienced since the Great Depression, is the collapse of the hyper-inflated real estate market, of which major contributors include the subprime morgtage boom largely mandated by the "Clinton Socialist Mission" imposed on FNM and FRE and made possible by the "Greenspan Easy Credit" expansionary monetary policy (i.e., low interest rates). This boom/bubble is deeply rooted in the secondary financial derivative markets in MBS, CDS, CDO, CDO Sqaure, and the like, largely powered by unregulated hedge fund speculations and greatly assisted by Cox's "Wall Street Friendly" SEC. Dr. Li's formula provided a convenient theoretical tool for the exponential explosion of such markets, nothing more, nothing less. The root cause of all of these is best summed up by the previous poster, "greed", which is as old as human being and will be the twin-brother of human beings for as long as there is such a thing as human being.

Human nature dictates that it is inevitable to get into such a blow-up mess that the world finds itself in now. It is not as easy to get out but the world collectively will ultimately find the exit. How? Yours truly wish to have the magic wants at my fingertips. Nonetheless, the following may help: 1) ridding mark-to-market accounting; 2) restoring the uptick rule; 3) banning naked short selling; and 4) imposing a maximum reserve ratio for banks.

The recession is still young, very young. Things WILL highly likely get worse, a lot worse, before getting better. Be confident, though, that things WILL ultimately get better. The key is finding the reflection point, which, yours truly feel, lies somewhere around the DOW at 6K and S&P 500 at 600 --- it takes Jesse Livermore-type eyes to foresee these kinds of reflection points and eventuality ahead of time. When and only when the aforementioned 4 measures go hand in hand, will yours truly go all in. This is not an issue of if but when and yours truly predict a timeline around the end of June - September 2009. Obama's stimulus package and spending/taxing budget are only digging deeper and deeper in a deep hole without the aforementioned measures being implemented hand in hand. And you read it here first.

The above are all my own personal humble opinions.
 
[FONT=宋体]一个稳定有效的资本和投资市场需要有完善的基础设施:会计上的[/FONT]mark-to-market accounting[FONT=宋体]只是一个方面;再有是我上面提出的简单易懂,中立的评级公司对风险的评级(当前评级公司为私利而混淆简单债券和节构性债券级别是罪魁祸首之一,且让然无更改意图);3)要有一个随时可得的市场价格信息,就是说你要买卖一种股票或金融证券,你必须先知道它当时的市场价值(而CDS,CDO的定价模型和发布控制在证券经济人和评级公司的手里,当投资者需要这些信息时,他们却人间蒸发,再不露面,无处线寻觅);最后,股票证券交易所强制要求挂牌机构每季度披露其财务市场信息,哪怕当时没有市场存在(根本没人敢买,愿意买任何债券),也要公布虚拟的市值损伤。如此,逼得几大银行发布(或记者造谣)每季度损失几十亿美元根本不存在亏损。加上卖空者的推波助澜,金融市场才降到当前的惨状。[/FONT]

[FONT=宋体]如果真感兴趣当前的金融危机,我推荐新出的一部文献记录片:[/FONT]"Inside the Meltdown"[FONT=宋体] [/FONT]
[FONT=宋体]可以译成:《金融市场崩溃的内幕》[/FONT]
[FONT=宋体]电影描述了从2007年夏季到2008年11月为止,华尔街和美国政府如何因为一系列的决策失误而走到今天的几乎无可挽回的地步(看了记录片,就会明白记者把此次金融危机归结到一个小小的定价模型是多么的幼稚可笑。我看写上述文章的记者不是外行充内行,就是想哗众取宠,制造震撼效应)。还好,李先生已海归回国了,不必担心成为千古罪人的危险。[/FONT]
[FONT=宋体][FONT=宋体]我本人基本同意记录片中编导者要表达看法和结论。[/FONT]
[/FONT]
Brown Bag Lunch - USA Housing Finance & Banking Fiasco: PBS Frontline's "Inside the Meltdown"Last week PBS provided a great analysis of the very recent history of the USA's housing finance tumble. Its focus is on the big players. What: PBS Frontline's Inside the Meltdown

General Link: --> FRONTLINE: inside the meltdown | PBS
Synopsis --> FRONTLINE: inside the meltdown: introduction | PBS
Transcript --> FRONTLINE: inside the meltdown: transcript | PBS
 
[FONT=宋体]真要感谢加京游子转贴的这篇有关李大卫博士的文章。花了几天研究李博士的理论和数学定价模型。也古狗了许多相关文章和评论。今天我终于悟出了此次金融危机的根源和发展过程。我准备抽时间写把自己的想法出来。遗憾的是,由于金融系统的复杂性,即使找出根源也无助于推导出解决方法。如同知道一个病入膏肓的人患了癌症,也不等于切掉癌症病造就可治愈(因为切除癌细胞以前病人可能就死了)。[/FONT]

[FONT=宋体]如果非要说此次金融危机与李博士的[/FONT]Gaussian copula function[FONT=宋体]的数学定价模型有什么间接的联系,那只能说李博士模型的两个前提假设条件即不符合实际,又违反了金融市场的后期发展,而没有人向市场和金融界明确指出(包括李博士本人可能也没意识到这个缺陷)。[/FONT]

[FONT=宋体]首先,李博士的整个模型建立在假设:投资者(市场)能正确给信用风险定价,即CDS当前的市场价格准确全面地反映了所有风险参数。所以从[/FONT]cds[FONT=宋体]价格中提取相关系数是准确唯一的。[/FONT]

[FONT=宋体]“[/FONT]Instead, he used market data about the prices of instruments known as credit default swaps.

he decided not to even bother trying to map and calculate all the nearly infinite relationships between the various loans that made up a pool. What happens when the number of pool members increases or when you mix negative correlations with positive ones? Never mind all that, he said. The only thing that matters is the final correlation number-one clean, simple, all-sufficient figure that sums up everything.[FONT=宋体]”(引自上文)[/FONT]

[FONT=宋体]其次,李博士和所有使用其模型的人假设这个神秘的相关系数是稳定的常量(如果是变量,模型则无法在实际操作中应用)。适用于今后若干年的信用衍生产品市场。[/FONT]

Li's approach made no allowance for unpredictability: It assumed that correlation was a constant rather than something mercurial.”(引自上文)

[FONT=宋体]在大学学习时导师告诫我们,经济学中数学模型的错误,无外乎两个方面:一个时数学(公式)推导的逻辑错误;另一个是其前提假设根本不成立。[/FONT]

[FONT=宋体]我们知道任何市场价格除了反映经济变量的内在关系,还受人们的供给和需求的影响。而后者更要受人们心理因素和对财富贪婪本性左右。举例想说,当房屋市场疯涨,达到泡沫的临界状态时,房价已经完全脱离成本和合理利润等相关关系,完全受人们投机心理所支配。但是李博士的模型仍然认为此市场价格是均衡价格,会长期保持下去。所以,第一假设不符合现实。[/FONT]

[FONT=宋体]再有,任何相关系数只是相对稳定,不可能是常量。当前整个系统风险出现,金融经济系统接近崩溃,所有相关系数都会有根本的改变。仍然以2004年的相关系数定价的[/FONT]cds[FONT=宋体]产品肯定不再适用,差之千里。第二个假设也不攻自破。[/FONT]

[FONT=宋体]当上述两个前提假设统统改变,建立在这两个假设上的模型,以及用模型算出的价格,和评级公司在此基础上给出的安全评级都土崩瓦解,灰飞烟灭。我很奇怪,如此浅显的错误为什么能蒙住专家学者的眼睛,忽悠市场如此长的时间。无论是李博士本人,还是有关人士都没有明确指出模型的缺陷。这该是金融理论界吸取的教训。[/FONT]

[FONT=宋体]当然当前危机的形成要远远超过一个脱离现实的定价模型造成的危害。还有更为复杂的市场和政策互动因素。[/FONT][FONT=宋体]我希望感兴趣的朋友可以一起讨论。[/FONT]
 
后退
顶部